Nuprl Lemma : rsqrt_square
∀[x:ℝ]. (rsqrt(x * x) = |x|)
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rabs: |x|,
req: x = y,
rmul: a * b,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsqrt_wf,
square-nonneg,
rmul_wf,
rleq_wf,
int-to-real_wf,
rabs_wf,
real_wf,
rmul_comm,
rsqrt-of-square,
zero-rleq-rabs,
req_functionality,
req_weakening,
req_inversion,
rabs-rmul,
rabs-of-nonneg,
rsqrt_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
applyEquality,
because_Cache,
sqequalRule,
independent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x:\mBbbR{}]. (rsqrt(x * x) = |x|)
Date html generated:
2017_10_03-AM-10_43_38
Last ObjectModification:
2017_08_27-PM-11_39_42
Theory : reals
Home
Index